Give an analysis of the time complexity $($use O$-$notation$)$ for each of the following program

segments by showing the steps $($Assume all variables used have been declared$)$:

$($i$)$ for $($i $=0$; i $<$ n$+100$; i$++)\{$

for $($j $=0$; j $<$ i$*$n; j$++)\{$

sum $=$ sum $+$ j;

$\}$

for $($k $=0$; k $<3$n; k$++)\{$

c$[$k$]=$ c$[$k$]+$ sum;

$\}$

$\}$